On quasi-linear Schrödinger-Poisson systems

Abstract

We study a high-field version of the periodic Schrödinger–Poisson system, for which the Poisson equation includes nonlinear terms corresponding to a field-dependent dielectric constant. Using a Galerkin scheme, we prove global existence and uniqueness, and present the matrix equations for the numerical evaluation of the potential. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.